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number of limit orders

The larger the number of limit orders at a given price level, the longer it will take a sequence of market buy orders to break through it. This increases the chances that just one market order to sell will come in, causing a reversal. Р РѕРі instance, in the case of the stock whose book is simulated in Table IV, we might expect with a preponderance of buy at market orders that the proportion of reversals after the sequence 33 4/8, 33 5/8 would be less than after the sequence 33 5/8, 33 6/8, because there are more limit orders (to sell) at 33 6/8 than at 33 5/8.

Further examination of Table IV reveals that the limit orders tend to cluster at the integer, half, quarters, and odd eighths in descending preference. This seems to be a prevailing characteristic of specialists' books (see legend, Table IV). We conclude from this discussion that reversals are more common at even eighths than at odd eighths, and more common at integers than half integers.

The mechanics of stock trading—as we have described them—are by no means peculiar to the New York Stock Exchange; they are closely matched on other American security exchanges, and they have their counterparts on the commodity exchanges. They may even have counterparts on other more or less organized competitive markets—say, stamps, coins, or used cars. These dealers must have both an inventory of cash with which to buy and an inven �tory of goods to sell. It may be instructive to compare the red and blue books of suggested buying and selling prices for used cars, and catalogues of market prices for U. S. stamps with the book of the specialist.

As reported above, the tendency to reversal has already been verified in coin and commodity markets. Numbers bookies frequently report clustering of numbers corresponding to some unusually symbolic event, and it is a common �place thing for the $2 issue of a set of stamps to sell for more than the $5 issue (e.g., most U.S. and U.N. series). Thus, clustering at round numbers probably holds in many other markets. We are not familiar with any experimental data in other markets on relative chances of continuation after previous continua �tions and reversals.

There are numerous casual competitors of dealers in these secondhand markets. In addition, want ads provide further competition and information. There are only two stocks in which competing dealers operate on the N.Y.S.E., and none on the A.S.E. For this monopoly privilege the specialist is required to maintain a fair and orderly market by trading for his own account when neces �sary. It should not be assumed that these transactions undertaken by the specialist, and in which he is involved as buyer or seller in 24% of all market volume, are necessarily a burden to him. Typically, the specialist sells above his last purchase on 83% of all his sales, and buys below his last sale on 81% of all his purchases [15, p. 84]. An insight into his technique will be presented below.

Let us imagine that the price of the stock has had a rise during the day's trading. The specialist or a floor trader might take a short position at 7/8, knowing that a considerable excess of buy market orders over sell orders would be needed to push the price through the 8/8 level, there being an excessive number of limit orders at 8/8. At the worst, the specialist could take a 1/8 point loss by buying at the 8/8 value after all of the sell limit orders on his book have been filled. Conversely, by taking a long position at 1/8 after a decline to that level, the specialist would have a chance to profit by his participation.

The New York Stock Exchange reports that one of the specialist's functions is to stabilize the market in his stock. They test this by the stabilization or "tick test." All specialists' purchases below the last different price and sales above the last different price arc considered stabilizing. The tendency to re �versal and clustering of limit orders explains why such contra-tick trading should be profitable.

Mr. Alfred Cowles added the following observation in a letter of March, 1965. "If professionals actually do habitually profit from a knowledge of these patterns, that might explain a phenomenon which for many years has intrigued me. As a result of repeated analyses of large numbers of purchases and sales made through various brokers for investors' accounts, I have noted repeatedly that the average price at which series of 104) or more orders have been executed consistently averaged at prices slightly less favorable to the investors than the average of high and low for the day for each stock purchased or sold." This is a manifestation of the compensation the specialist receives for the stabilizing services he performs to investors. [See 13, p. 103.]